Aren't you forgetting that the efficiency of a thermodynamic process is proportional the ratio of the differences in temperature and the ambient. If the Bitcoin mining chip is not as hot as the coils, then it will not be as efficient as the coils were. Also for example a hair dyer needs all the heat transfered within a short period of time, and if the heat transfer is slow not all of the heat may be extracted to the hair and instead wasted to the ambient. So somewhat less than free mining.